Adaptive mesh refinement simulations of a galaxy cluster merger - I. Resolving and modelling the turbulent flow in the cluster outskirts

The outskirts of galaxy clusters are characterized by the interplay of gas accretion and dynamical evolution involving turbulence, shocks, magnetic fields and diffuse radio emission. The density and velocity structure of the gas in the outskirts provide an effective pressure support and affect all processes listed above. Therefore, it is important to resolve and properly model the turbulent flow in these mildly overdense and relatively large cluster regions; this is a challenging task for hydrodynamical codes. In this work, grid-based simulations of a galaxy cluster are presented. The simulations are performed using adaptive mesh refinement (AMR) based on the regional variability of vorticity, and they include a subgrid scale (SGS) model for unresolved turbulence. The implemented AMR strategy is more effective in resolving the turbulent flow in the cluster outskirts than any previously used criterion based on overdensity. We study a cluster undergoing a major merger, which drives turbulence in the medium. The merger dominates the cluster energy budget out to a few virial radii from the centre. In these regions, the shocked intra-cluster medium is resolved and the SGS turbulence is modelled, and compared with diagnostics on larger length-scale. The volume-filling factor of the flow with a large vorticity is about 60 per cent at low redshift in the cluster outskirts, and thus smaller than in the cluster core. In the framework of modelling radio relics, this point suggests that upstream flow inhomogeneities might affect preexisting cosmic-ray population and magnetic fields, and the resulting radio emission.